Viscoelastic inhomogeneous beam under time-dependent strains: A longitudinal crack analysis

Abstract

The present paper is concerned with analysis of two longitudinal cracks in a viscoelastic inhomogeneous cantilever beam. The loading of the beam is applied by two stages. At the first stage, the strains increase with time at a constant speed up to a given magnitude. At the second stage, the strains remain constant with time. The viscoelastic behavior of the beam is described by using a viscoelastic model with a linear spring in series with a linear dashpot and a second linear dashpot connected parallel to the spring and the first dashpot. Stress-strain-time relationships of the viscoelastic model are derived for both stages (at increasing strain and at constant strain with time). Time-dependent strain energy release rates are obtained for both longitudinal cracks by analyzing the balance of the energy. Solutions to the time-dependent strain energy release rate are derived also by considering the time-dependent strain energy stored in the beam structure. The solutions are used to analyze the change of the strain energy release rate with time at both stages of loading.